Problem: The sum of two numbers is $71$, and their difference is $23$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 71}$ ${x-y = 23}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 94 $ $ x = \dfrac{94}{2} $ ${x = 47}$ Now that you know ${x = 47}$ , plug it back into $ {x+y = 71}$ to find $y$ ${(47)}{ + y = 71}$ ${y = 24}$ You can also plug ${x = 47}$ into $ {x-y = 23}$ and get the same answer for $y$ ${(47)}{ - y = 23}$ ${y = 24}$ Therefore, the larger number is $47$, and the smaller number is $24$.